Tuesday, 16 October 2012

The Shapley-Roth Nobel

The prize was awarded "for the theory of stable allocations and the practice of market design". The Swedish Academy has awarded a few prizes in game theory and mechanism design recently,* so this one came as a bit of a surprise to me. In the office pool, my three guesses were Shiller (likely in combination with Fama for financial markets); Tirole (industrial organisation); or, Gordon Tullock and Anne Krueger for rent-seeking. The last was mostly wishful thinking.

Shapley is famous for the "Shapley Value"** - a solution for surplus-sharing among players in a cooperative game. The Shapley-Shubik power index occasionally shows up in applications in public choice. Shapley also is known for having developed matching algorithms with some rather desirable characteristics: the Gale-Shapley algorithm results in stable matches. A set of stable matches obtains when no pair, matched with other partners, would mutually wish to break their current matches for a new partnership. Roth extended the algorithm and applied it pretty ingeniously to help save lives.

What Roth has done is extend the Gale-Shapley algorithm to more complicated matches and to actually design such algorithms to solve real problems. In the 1970s, for example, the medical residency algorithm began to run into trouble because of a new development, the dual career couple. How to match couples, both doctors, to hospitals in the same city? By the 1990s assortative matching in the marriage market was beginning to derail matching in the doctor-hospital market! Roth was called in to solve the problem and moved from being a theorist to a market designer. Roth and Peranson designed the matching algorithm that is now used by Orthodontists, Psychologists, Pharmacists, Radiologists, Pediatric surgeons and many other medical specialties in the United States.

Most famously, Roth has worked on improving kidney allocation. I first wrote about this in 2004 (see also these posts):

Your spouse is dying of kidney disease. You want to give her one of your kidneys but tests show that it is incompatible with her immune system. Utter anguish and frustration. Is there anything that you can do? Today the answer is yes. Transplant centers are now helping to arrange kidney swaps. You give to the spouse of another donor who gives to your spouse. Pareto would be proud. Even a few three-way swaps have been conducted.

But why stop at three? What about an n-way swap? Let’s add in the possibility of an exchange that raises your spouse on the queue for a cadaveric kidney. And let us also recognize that even if your kidney is compatible with your spouse’s there may be a better match. Is there an allocation system that makes all donors and spouses better off (or at least no worse off) and that maximizes the number of beneficial swaps? Inan important paper (Warning! Very technical. Requires NBER subscription.) Alvin Roth and co-authors describe just such a mechanism and show that it could save many lives. Who says efficiency is a pedestrian virtue?

Since that time we have seen many such swaps including this record of 60 people and 30 kidneys. Truly a noble match.

Al Roth has been a bit on my mind lately as well. The University of Canterbury is considering mandating some kind of cultural competence requirements for students (maybe for faculty too, who knows); we're busily documenting how we're already incorporating cultural things into our courses.

In my Economics and Current Policy Issues course, we spend a week on the economics of organ transplantation. I there note the many ways we can improve upon the current system, ranging from presumed consent systems to compensation for cadaveric organ donation, then on to compensation for live organ donors (kidney, liver lobe), and, potentially, full but regulated markets in organs. And I touch on Al Roth's work on repugnance constraints. Even if we can prove that a well-designed, well-regulated market in organs would save thousands of lives, cultural constraints among voters make some of those those solutions impossible; Roth tries to design mechanisms that route around that inefficiency. I suppose I ought to add Roth's paper to the recommended readings for that week and tick the "cultural competence" box in a productive way.

Congrats to Shapley and Roth. And, hopefully next year, congratulations to Tullock and Krueger.***

* 2007 to Hurwicz, Maskin and Myerson (mechanism design); 2005 to Aumann and Schelling (game theory); 2002 to Kahneman and Smith (the Smith half was for experimental economics).

** The calculation of which was something I desperately hoped would not show up on my micro prelims. Fortunately, it didn't.

*** Tullock is a year older than Shapley - he turned 90 this year. If Stockholm is just waiting out the clock so they can award the prize to Krueger alone, I hope Tullock's ghost haunts them forever, pestering them with insults, derisive comments about their intelligence, and tangential remarks about ancient China whenever they're trying to concentrate on anything.

1 comment:

I wouldn't be surprised if they were waiting out Tullock's death, I don't think they ever got over Gunnar Myrdal calling for the abolition of the award for forcing him to share it with the "reactionary" Hayek!